An Order of Magnitude (abbreviated to OoM) is a measurement of how many times you need to multiply ten by itself to get to a number. Using logarithms, you can instead see what you need to raise ten to the power of, to get non-integer Orders of Magnitude.
In Egg, inc. Edit
In Egg, inc., the Farm Value is measured in orders of magnitude. This allows for easier comparison, because 1036 and 1042 are easier to compare than 1,000,000,000,000,000,000,000,000,000,000,000,000 and 100,000,000,000,000,000,000,000,000,000,000,000,000,000. With Orders of Magnitude, you don't have to painstakingly count the zeroes, you can just say, '42-36=6, so the second number is 106=1 million times the first!'
In Science Edit
When comparing extremely large things like stars or extremely small things like bacteria, if there are hundreds of billions of bacteria in a human or trillions of stars in the galaxy or septillions of atoms in a gram of water (6.02214085774×1023), it gets confusing to count the zeroes every time you want to know the exact size of an extremely large or small number, so scientists use Orders of Magnitude for those.
To calculate a number in OoM, you use the equation, log10(number). A logarithm is like saying, 'How many times do I need to multiply the base number (the little one at the start) by itself to get the second one?', and is symmetrical with an exponent ('What do I get when multiply this number by itself this many times?') or a root ('What do I multiply by itself this many times to get this number?'), and there's an idea to remove all of these symbols and words and use a triangle instead.